He says that 40,000 licensed drivers and the estimated 3.5 million Londoners who have used Uber "are depending on us."

London's transport authority said it doesn't like the company's approach to reporting serious crimes. Also at issue: a controversial piece of software called "Greyball" that prevents regulators and law enforcement from monitoring Uber's app.

Khosrowshahi took over as Uber's top exec last month. He inherited several battles from his predecessor, Kalanick.

The backlash against the company in London isn't an isolated incident. Uber has faced regulatory troubles in markets across the globe — including in U.S. cities like Austin, Texas and Portland, Oregon and in European countries, including Hungary and Italy.

Kalanick also left behind the fallout from a PR crisis that was kicked up earlier this year amid allegations that managers didn't adequately address reports of sexual harassment.